I've lived in the east all my life and have always liked the Appalachians, but I was just in CO and have to say the Rockies are amazing in their own way. There's just so many more levels to the terrain in the Rockies. You start out at valley level and keep going up and up and you go past fir forests, alpine lakes, tundra, etc. Its kinda boring as there's only fir trees but usually the more extreme weather makes up for it. For instance I went up Mt Evans and it was 65'ish at the base but 35*F and snowing at the peak in the middle of summer. You don't experience that in the Apps unless you're on Mt. Washington.
What I don't like about the Rockies is that the elevation can be too much. It takes entire days to hike up mountains there, and the increased elevation and massive views can be daunting. Its not that relaxing... that and I don't like how they're mostly desert/dry terrain. And I don't like their geology as much as the Apps. With the Rockies they don't seem to be such a continuous range, there's clusters of mountains seperated by vast stretches of flat desert/grassland, and I believe they originated by uplift and erosion of their plateau? I like the folded appearance of the Apps more its more reminiscent of a continental collison which seems to be more striking overall. Its like individual mountains in the Rockies can be much more awe-inspiring but I consider the Apps to be more awe-inspiring as a whole. IIRC the Apps were much more of a barrier to western settlement than the Rockies were, with their dense forests and never-ending arrays of parallel ridges. I'm not sure if you could ever consider hills to be that much of a barrier to movement?
Those who knock the Apps, they're real mountains. Someone quoted the highest mountain in Texas as being higher than anything back east....but it sits on a 5700' plateau with only 3000' of prominence. Mt. Mitchell and Mt. Washington are both on the list of "ultra" prominent mountains worldwide with over 6000' of prominence each. To me that is what makes a mountain, the difference between it and the landscape. I've seen Denali in Alaska and its so prominent you can see it over the curvature of the Earth, hundreds of miles away in Fairbanks. The 14'ers in the Rockies sure look amazing but they're only about 8000' of prominence on a 5000-6000' plateau which is only 2000-3000' more prominent than Mitchell and Washington.
I also like the Apps because of their diversity, it reminds me of what I've heard about mountains in Central America, how you can have tropical conditions at the base and increasingly temperate and cool as you go up in elevation. In the Apps you can start out with southern pine in the valleys, moving up to deciduous forests and eventually fir forests at the very peaks. There's a LOT of diversity in the forests. The fir at the peaks also remind me of the fir on the lower elevations of the Rockies and gives the tops of the highest southern Apps an alpine feel. Also they can be dramatic, try going up I-77 from NC to the mountains in VA near Mt. Rogers, its very much like going up I-70 from Denver into the Rockies. Approaching the N. Ga mountains from Atlanta on 400 or I-575 always looks dramatic as well, the mountains loom tall in the distance from a ways away as you approach. Also, standing on the summit of Grandfather Mountain in NC can be almost as dizzying as being on Mt. Evans. And like how I saw snow on Mt. Evans in summer, the Wikipedia article for Mt. Mitchell
https://en.wikipedia.org/wiki/Mount_Mitchell states that flurries can be seen on the summit even in July, at the same latitude and only miles away from Raleigh, NC which can be 90-100*F that same day. Sure the 6000 footers in the Apps aren't mountains, lol.
I've been to the UK and consider Ben Nevis and Snowdon and others to be mountains and they're smaller than the Appalachians. They're supposed to be of a similar origin to the Apps, along with the Atlas in Africa and the mountains in Scandinavia which I think also adds some awe to the Apps, that you can basically see the chain on both sides of the Atlantic.
I've also enjoyed skiing in the Apps, its more technical and less fast, and imperfect conditions can be more challenging. Going down the black diamonds on Snowshoe or Sugar mountain can be epic in their own way. I've also experienced conditions that reminded me of being in the Sierra Nevada. Raining/sleeting in the mountain valleys, but blizzard conditions and fresh powder (FEET of snow) as you get up the mountain and on the ski resort. Hills just don't have those sort of characteristics.